The height of a cone is 30 cm .A small cone is cut off at the top by a plane parallel to the base . If its volume be `(1)/(27)` of the volume of the given cone, at what height above the base the section has been made?

Explanation

To solve the problem, we need to find the height above the base at which a small cone is cut off from a larger cone. The height of the larger cone is given as 30 cm, and the volume of the small cone is \( \frac{1}{27} \) of the volume of the larger cone.

### Step-by-Step Solution:

1. **Understand the relationship between the volumes of the cones**:
The volume \( V \) of a cone is given by the formula:
\[
V = \frac{1}{3} \pi r^2 h
...